Problem: Simplify the following expression: $\sqrt{208}+\sqrt{325}+\sqrt{117}$
First, try to factor any perfect squares out of the radicals. $= \sqrt{208}+\sqrt{325}+\sqrt{117}$ $= \sqrt{16 \cdot 13}+\sqrt{25 \cdot 13}+\sqrt{9 \cdot 13}$ Separate the radicals and simplify. $= \sqrt{16} \cdot \sqrt{13}+\sqrt{25} \cdot \sqrt{13}+\sqrt{9} \cdot \sqrt{13}$ $= 4\sqrt{13}+5\sqrt{13}+3\sqrt{13}$ Finally, simplify by combining the terms. $= ( 4 + 5 + 3 )\sqrt{13} = 12\sqrt{13}$